The number of securities giving the maximum return in the presence of transaction costs

An essential element of any realistic investment portfolio selection is the consideration of transaction costs. Our purpose, in this paper, is to determine the maximum return and the corresponding number of securities to buy giving such return, whenever practical constraints features related to budget, buy-in thresholds, and transaction costs are taken into consideration. Dealing with the portfolio selection and optimization problem in the point of view of individual investors, we will arrive to get an analytic result, leading to a new and simple alternative solution to heuristic algorithms. Moreover, this result can be considered as another approach to integer optimization.